Conditional dissociation as a punishment mechanism in the evolution of cooperation

• The effect of conditional dissociation on the evolution of cooperation is investigated.
• Cooperation level is lowered when mixed strategies are allowed.
• Two monomorphic equilibria exist, one is cooperative but intolerant and the other is defective and tolerant.
• Longer lifespan and longer waiting time favor cooperation.

Recent studies show that conditional dissociation, a.k.a. post-interaction partner-refusal, can promote the emergence and stability of cooperation. However, in most of these studies, players’ strategies are restricted to pure ones, which is obviously inconsistent with many biological and economic situations. Another concern with line of these studies is that conditional dissociation is often combined with other mechanisms. These mechanisms may favor cooperation per se, leaving it unclear whether conditional dissociation is indeed a key factor. In this paper, we study a clean model, pruning all the factors other than conditional dissociation that may favor cooperation. We find that conditional dissociation, which could be viewed as a variant of peer punishment, does promote cooperation, no matter whether mixed strategies are allowed or not. This confirms the previous findings in the literature. In addition, compared with the pure strategy scenario, cooperators are less competitive when mixed strategies are allowed. Our main finding is supported by both the numerical simulations and the theoretical analysis of Neutrally Stable Strategy. We also find that cooperative behavior is favored when waiting time and/or the population’s lifespan are longer.